Related papers: The finite representation property for composition…
The First and Second Representation Theorem for sign-indefinite quadratic forms are extended. We include new cases of unbounded forms associated with operators that do not necessarily have a spectral gap around zero. The kernel of the…
We prove that over an algebraically closed field there is a representation embedding from the category of classical Kronecker-modules without the simple injective into the category of finite-dimensional modules over any…
We give an extension to a nonconvex setting of the classical radial representation result for lower semicontinuous envelope of a convex function on the boundary of its effective domain. We introduce the concept of radial uniform upper…
We present a conjecture on the irreducibility of the tensor products of fundamental representations of quantized affine algebras. This conjecture implies in particular that the irreducibility of the tensor products of fundamental…
We show that under natural and quite general assumptions, a large part of a matrix for a bounded linear operator on a Hilbert space can be preassigned. The result is obtained in a more general setting of operator tuples leading to…
This paper presents analogous results of Hua [7][8] on numbers of representations of quivers over finite fields which respect nilpotent relations under certain assumptions. A closed formula which counts isomorphism classes of absolutely…
The problem of expressing a specific polynomial as the determinant of a square matrix of affine-linear forms arises from algebraic geometry, optimisation, complexity theory, and scientific computing. Motivated by recent developments in this…
We prove that any equational basis that defines RRA over wRRA must contain infinitely many variables. The proof uses a construction of arbitrarily large finite weakly representable but not representable relation algebras whose "small"…
In this paper we analyze the notion of morphisms of rings of superfunctions which is the basic concept underlying the definition of supermanifolds as ringed spaces (i.e. following Berezin, Leites, Manin, etc.). We establish a representation…
We prove that partially ordered set has finite number of finite-dimensional indecomposable nonequivalent Hilbert representations with orthoscalarity condition if and anly if it has finite number of indecomposable linear representations. We…
We study the degree of irreducible morphisms in any Auslander-Reiten component of a finite dimensional algebra over an algebraically closed field. We give a characterization for an irreducible morphism to have finite left (or right) degree.…
We look at spaces of infinite-by-infinite matrices, and consider closed subsets that are stable under simultaneous row and column operations. We prove that up to symmetry, any of these closed subsets is defined by finitely many equations.
It is well-known that characters classify linear representations of finite groups, that is if characters of two representations of a finite group are the same, these representations are equivalent. It is also well-known that, in general,…
We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F, or more generally, of a bounded PAC field F. This paper answers some of the questions of [1], and in particular that any finite group…
We deal with the classification problem of finite-dimensional representations of so called Askey--Wilson algebra in the case when $q$ is not a root of unity. We classify all representations satisfying certain property, which ensures…
In this note, we initiate a study of the finite-dimensional representation theory of a class of algebras that correspond to noncommutative deformations of compact surfaces of arbitrary genus. Low dimensional representations are investigated…
We prove that two finite-dimensional commutative algebras over an algebraically closed field are isomorphic if and only if they give rise to isomorphic representations of the category of finite sets and surjective maps.
We classify and construct irreducible completely splittable representations of affine and finite Hecke-Clifford algebras over an algebraically closed field of characteristic not equal to 2.
A notion of Drinfeld polynomials is introduced for modules of two-parameter quantum affine algebras. Finite dimensional representations are then characterized by sets of $l$-tuples of pairs of Drinfeld polynomials with certain conditions.
The present paper mainly considers the representation type of the enveloping algebra of monomial algebra. Let $A$ be a monomial algebra and $A^e= A\otimes_{\mathrm{l}\!\mathrm{k}} A^{\mathrm{op}}$ its enveloping algebra. It is shown that…